Question: Solve for $x$ and $y$ using substitution. ${-4x-5y = -9}$ ${y = -2x+3}$
Solution: Since $y$ has already been solved for, substitute $-2x+3$ for $y$ in the first equation. ${-4x - 5}{(-2x+3)}{= -9}$ Simplify and solve for $x$ $-4x+10x - 15 = -9$ $6x-15 = -9$ $6x-15{+15} = -9{+15}$ $6x = 6$ $\dfrac{6x}{{6}} = \dfrac{6}{{6}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -2x+3}\thinspace$ to find $y$ ${y = -2}{(1)}{ + 3}$ $y = -2 + 3$ $y = 1$ You can also plug ${x = 1}$ into $\thinspace {-4x-5y = -9}\thinspace$ and get the same answer for $y$ : ${-4}{(1)}{ - 5y = -9}$ ${y = 1}$